I use Edge Tapmatic Liquid by LPS (available at MSC) and a Starrett tap handle #174 for taps as small as 000-120 in SST, Ti and AL. ...I have not tapped 8620, but in the annealed state it shouldn't be any more difficult than the materials I've tapped above. Edge is fairly expensive, but a little goes a long way and it is absolutely much cheaper than breaking taps and fixing parts.
Don't buy your taps from the local hardware store! Buy good HSS (coated or not depending on app) from a good tool distributor. The hardware store variety taps are fine for chasing threads, but suck at actually cutting new threads.